Algorithms that compute rows of \(D\)  in a lazy fashion need not delete or simplify rows of \(D\)  at all; they can simply skip over them. This saves not only algebraic operations (which would otherwise have been needed to reduce a row to zero), but also the computations needed to construct that row in the first place. The pairing of lazy methods with this clearing optimization was pioneered in [1]}. In numerical experiments, the time and memory saved by excluding rows indexed by \(\mathrm {val}(\mu )\)  is disproportionate to the number of rows excluded [2]}, [3]}, [1]}, [5]}, at least for clique complexes. Effects for cubical complexes tend to be nontrivial but less pronounced [6]}. The reason for these empirical trends is a matter of ongoing research; see [1]} for a nice review. New experimental evidence is reported in §.
